# CRPropa 3.1 -- A low energy extension based on stochastic differential equations

## TL;DR

This paper introduces CRPropa 3.1's new stochastic differential equation module for simulating low-energy cosmic ray propagation, enabling anisotropic diffusion modeling in complex magnetic fields with validated accuracy.

## Contribution

The paper presents a novel low-energy propagation module in CRPropa 3.1 that uses stochastic differential equations to model anisotropic diffusion in cosmic ray transport.

## Key findings

- Validated the accuracy of the new diffusion algorithm.
- Demonstrated the impact of diffusion coefficient ratios on cosmic ray density.
- Explored the influence of particle rigidity on diffusion behavior.

## Abstract

The propagation of charged cosmic rays through the Galactic environment influences all aspects of the observation at Earth. Energy spectrum, composition and arrival directions are changed due to deflections in magnetic fields and interactions with the interstellar medium. Today the transport is simulated with different simulation methods either based on the solution of a transport equation (multi-particle picture) or a solution of an equation of motion (single-particle picture). We developed a new module for the publicly available propagation software CRPropa 3.1, where we implemented an algorithm to solve the transport equation using stochastic differential equations. This technique allows us to use a diffusion tensor which is anisotropic with respect to an arbitrary magnetic background field. The source code of CRPropa is written in C++ with python steering via SWIG which makes it easy to use and computationally fast. In this paper, we present the new low-energy propagation code together with validation procedures that are developed to proof the accuracy of the new implementation. Furthermore, we show first examples of the cosmic ray density evolution, which depends strongly on the ratio of the parallel $\kappa_\parallel$ and perpendicular $\kappa_\perp$ diffusion coefficients. This dependency is systematically examined as well the influence of the particle rigidity on the diffusion process.